Elsevier

Signal Processing

Volume 80, Issue 12, December 2000, Pages 2617-2621
Signal Processing

A new optimal digital halftoning technique based on the discrete cosine transform

https://doi.org/10.1016/S0165-1684(00)00143-2Get rights and content

Abstract

Digital halftoning is a technique to display a gray-level image with a bilevel device. Conventionally, most halftoning techniques are done in the spatial domain. A new halftoning technique based on the discrete cosine transform is proposed. The method chooses an optimal bilevel image to display the original gray-level image and minimize the weighted mean square error based on the discrete cosine transform domain. The simulation results indicate that our algorithm can produce very good halftoned images without false contours.

Zusammenfassung

Digitale Halbtönung ist eine Technik, um grauwertige Bilder mit einer zweiwertigen Abbildung herzustellen. Es wird eine neue Halbtönungstechnik vorgeschlagen, die sich auf die diskrete Cosinustransformation stützt. Die Methode wählt eine optimale zweiwertige Abbildung, um das originale Graubild herzustellen und minimiert den gewichteten mittleren quadratischen Fehler im Transformationsbereich der diskreten Cosinustransformation. Die Simulations-ergebnisse zeigen, daß unser Algorithmus sehr gute halbgetönte Bilder ohne falsche Konturen herstellen kann.

Résumé

La demi-teinte numérique est une technique permettant d'afficher une image en niveaux de gris avec des dispositifs à deux niveaux. De façon conventionnelle, la plupart des techniques de demi-teinte sont faites dans le domaine spatial. Nous proposons une nouvelle technique de demi-teinte basée sur la transformée en cosinus discrets. La méthode choisit une image à deux niveaux optimale pour afficher l'image originale en niveaux de gris et minimise l'erreur quadratique moyenne pondérée sur base du domaine de la transformée en cosinus discrets. Les résultats de simulation indiquent que notre algorithme peut produire de très bonnes images en demi-teintes sans faux contours.

Introduction

Many displaying devices are basically bilevel in nature. The displaying cell is either on or off, bright or dark, white or black. Digital halftoning is a technique that displays a gray-level image with two levels [1], [6], [16]. Digital halftoning techniques can be done in the spatial domain or in the frequency domain. The techniques can be classified into the point methods [9], [10], [11], [12], [13], the neighborhood methods [2], [4], [5], [7] and the search methods [3], [8], [17]. The point methods and the neighborhood methods are done in the spatial domain, while the search methods can be done either in the spatial domain [14], [15] or in the frequency domain [3], [8], [17].

In the point methods, Bayer [2], Lippel [9], [11], [12] and Limb [10] developed their methods for two level rendition of continuous image. Mitsa and Parker [13] used a blue-noise mask to halftone a gray-level image. In the neighborhood methods, error diffusion [5] is a well-known method to solve the false contouring problem. It uses neighborhood operations to diffuse the error over a weighted neighborhood. The shortcoming of this algorithm is that the error between each bilevel pixel and its original pixel is dispersed to its neighborhood. Eschbach and Knox [4] proposed an error diffusion algorithm with edge enhancement.

In the search methods, Pappas [14], [15] used a least-squares model-based halftoning method for both B&W and color printers which incorporates the properties of the display device and human visual system in the spatial domain. Carnevali et al. [3] used simulated annealing and Kollias [8] used a unified network for digital image halftoning based on the minimization of the weighted mean squared error in the frequency domain of the discrete Fourier transform. Zakhor [17] also proposed a new class of digital halftoning techniques with linear programming based on the discrete Fourier transform. Instead of using the discrete Fourier transform, most video coding techniques such as JPEG, MPEG I, MPEG II and HDTV use the discrete cosine transform (DCT). Since the DCT just computes real numbers it is much faster than the discrete Fourier transform, which computes complex numbers. This paper proposes a new digital halftoning algorithm based on the DCT. By our algorithm, the image can be divided into small subimages in order to reduce computational complexity. An optimal bilevel subimage is obtained by minimizing the distortion between the bilevel subimage and its corresponding gray-level subimage in the DCT domain. The optimization exhaustively searches for the optimal bilevel subimage with the least mean square error to replace the gray-level subimage. By our experimental results, not only are the edges in the halftoned image enhanced, but also the false contours are greatly reduced.

Section snippets

The proposed algorithm

Given a gray-level image, a digital halftoning algorithm can be stated as below.

Find a bilevel image that gives the illusion of a gray-level image on a bilevel display.

In the bilevel image, we shall call the pixel “1-pixel” if its gray-level is equal to 1; otherwise it is called “0-pixel”. There are two problems to find an optimal bilevel image. One is how many 1-pixels are needed in the optimal bilevel image. The other is how to distribute these 1-pixels over the image. For the first question,

Simulation

Four images of 512×512 are halftoned and printed on a laser printer with 300dpi. Fig. 2 shows the halftoned images based on the proposed algorithm with the weighting coefficients given in Eq. (10). These bilevel images are very smooth without contouring effect.

Conclusions

We proposed a new binary optimization technique for digital halftoning. The proposed algorithm minimizes the distortion between the gray-level image and the halftoned image in the DCT domain. It is much faster than Zakhor's algorithm. It greatly reduces false contouring, and produces a very smooth halftoned image.

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